In Aperture, the smaller the number means the larger the aperture.
The aperture of F/4.0 is larger than F/5.6
So if you are looking for a lens that can produce an image that the subject is in focus, the background is out of focus, you can look for a FAST lens in which has a smaller Maximum Aperture (i.e. F/1.8)
Also a telephoto lens can produce the blur background effect with a relatively larger aperture setting (i.e. F/5.6)
But you may need to read more about Depth of Field. It is because a large aperture will not guarantee you such effect. For example, you use a 50mm F/1.8 lens and shoot at F/1.8 aperture. The subject is 100ft away from your camera and the background is about 150ft away from the camera. You may notice that both the subject and the background are in focus.